Charged clusters in strongly correlated electron gas

We examine a mixture of electrons and holes in semiconductors. It is well known that in such a system the effective Coulomb interaction is perfectly screened at long distances, which leads to Mott's metal-insulator phase transition. We show that the screening is not monotonic and at intermediate ranges there are regions of over-screening, which at low densities become strong enough to destroy the homogeneous mixture by clustering charges. We suggest that this phenomenon is responsible for the broad density distribution of the electron-hole liquid and the condensed plasma phase in silicon suggested by Smith and Wolfe (1995 Phys. Rev. B 51 7521). When the hole mass is set equal to the proton mass we can study properties of the metallic hydrogen and show that at high pressures there is a phase transition into a crystal phase of protons.